Résumé : Daugavet- and Delta-points are natural localizations of geometric characterizations of the Daugavet property and of spaces with bad projections (also known as spaces with the diametral local diameter two property). An element $x$ in the unit sphere of a Banach space $X$ is called a Daugavet-point if every slice of the unit ball of $X$ contains elements which can be taken at distance arbitrarily close to 2 from the point $x$, and it is called a Delta-point if it only satisfies this requirement for slices containing $x$. Since their introduction those points have been systematically studied in classical Banach spaces, and surprising nonintuitive examples of Banach spaces with strong seemingly opposite isomorphic properties in which Daugavet-points exist have been discovered. In this talk we look for isometric properties providing an obstruction to the existence of Daugavet- and Delta-points in a given Banach space. In particular we study the influence of the asymptotic geometry of a Banach space on the existence of those points and we provide new examples of Banach spaces which fail to contain them.
Résumé : This talk will be split in two parts. The first one will be dedicated to introducing the definitions of compact quantum groups in the sense of Woronowicz, and some objects of noncommutative probability. In the second one it will be extended the purely algebraic setting of noncommutative Lévy processes to the analytic case by simply exploiting the fact that in the classical version the whole information is encoded in the corresponding convolution semigroup. In fact, we prove that Lévy processes on compact quantum groups actually exist via the generalization of the theory set by Hudson and Parthasarathy. Further, an analogue to the characterization of Lévy processes on involutive bialgebras, made by means of Schürmann’s theory, will be presented for the context of compact quantum groups. Finally, it is shown that there exists a one-to-one correspondence between norm continuous quantum Lévy processes and the Fock-space ones.
Lieu : LmB, salles 316B et 316Bbis
Lieu : UFR ST, Besançon
Lieu : Salle 335B
Lieu : Besançon, UFR ST, Amphi B
Lieu : Salle 309B